Paint spray particle trajectory analysis method and system

ABSTRACT

A system and method of analyzing paint spray particle trajectory on a vehicle with a computer aided design (CAD) model representative of the vehicle. The method includes the steps of preparing a CAD model of a desired portion of the vehicle and placing a paint spray gun at a desired location with respect to the desired portion of the vehicle. The method also includes the steps of specifying a set of particle information describing particles to be sprayed from the paint spray gun and computing a trajectory for a particle stream emanating from the paint spray gun. The method further includes the steps of displaying the trajectory relative to the desired portion of the vehicle on a display to permit visual observation thereof and relocating the paint spray gun if necessary to achieve a desired trajectory.

BACKGROUND OF THE INVENTION

[0001] 1. Field of the Invention

[0002] The present invention relates generally to computer aided vehicledesign and, more specifically, to a method and system of paint sprayparticle trajectory analysis for computer aided vehicle design.

[0003] 2. Description of the Related Art

[0004] There are numerous computer related tools which can facilitatethe design and testing of vehicles such as motor vehicles, includinggeneralized software programs such as computer aided engineering (CAE),computer aided design (CAD), and computational fluid dynamics (CFD).These tools are typically used to investigate many issues related tovehicle design, including vehicle durability, vehicle performance, andvehicle aerodynamics. Heretofore, limitations on computer speed andalgorithm accuracy have inhibited the development of a particletrajectory analysis tool in which several exterior aerodynamic designissues can be studied.

[0005] Paint application operations amount to a significant fraction ofthe total manufacturing cost of new vehicles. Improvements in thepainting process can wsnot only reduce the manufacturing cost butimprove appearance and durability, which directly influences customersatisfaction, and warranty costs. One metric for improvements in thepainting process is the Paint Transfer Efficiency (PTE) which is ameasure of how well paint is transferred from a bell applicator of apaint spray gun to a body of the vehicle. Increases in PTE effect paintquality and costs while simultaneously reducing paint waste andemissions. With demands to reduce vehicle costs and emissions, newtechnologies are being developed to determine bell applicator andpaintbooth designs. Computation Fluid Dynamics (CFD) is one technologythat can aid in quickly determining PTEs under various operatingconditions (e.g. shaping air velocity, bell angular velocity and fluidflow, and paintbooth downdraft velocity).

[0006] With the advent of new and improved CFD technology, an accurateexternal flow field can now be calculated, thus making a particletrajectory analysis tool technically possible. As a result, it isdesirable to provide a system and method for paint spray trajectoryanalysis to aid in vehicle design. It is also desirable to have aprocess to improve paint transfer efficiency for bell sprayers of paintspray guns. It is further desirable to provide a process that willdetermine particle trajectories of paint particles under the influenceof drag, gravity and electrostatic potential.

SUMMARY OF THE INVENTION

[0007] Accordingly, the present invention is a system and method ofanalyzing paint spray particle trajectory on a vehicle with a computeraided design (CAD) model representative of the vehicle. The methodincludes the steps of preparing a CAD model of a desired portion of thevehicle and placing a paint spray gun at a desired location with respectto the desired portion of the vehicle. The method also includes thesteps of specifying a set of particle information describing particlesto be sprayed from the paint spray gun and computing a trajectory for aparticle stream emanating from the paint spray gun. The method furtherincludes the steps of displaying the trajectory relative to the desiredportion of the vehicle on a display to permit visual observation thereofand relocating the paint spray gun if necessary to achieve a desiredtrajectory.

[0008] One advantage of the present invention is that a method andsystem of analyzing paint spray particle trajectory is provided whichpermits modification of vehicle design based upon computed particletrajectories with respect to a CAD model of the vehicle. Anotheradvantage of the present invention is that the method and system enablesdynamic placement of a paint spray gun into a flow domain to permitvisual observation and alteration of resulting paint particletrajectories with respect to a CAD model representative of the vehicle.Yet another advantage of the present invention is that the method andsystem allows a user to specify various characteristics of a paint spraygun including visually placing it near the vehicle, prescribing dropletsize and density, spray angle and velocity, and then computing anddisplaying spray trajectories. Still another advantage of the presentinvention is that the method and system determines paint particletrajectories under the influence of drag, gravity and electrostaticpotential.

[0009] Other features and advantages of the present invention will bereadily appreciated as the same becomes better understood after readingthe subsequent description taken in conjunction with the accompanyingdrawings.

BRIEF DESCRIPTION OF THE DRAWINGS

[0010]FIG. 1 is a flowchart of a method, according to the presentinvention, of analyzing paint spray trajectory.

[0011]FIG. 2 is a flowchart of a method, according to the presentinvention, to aid in designing a vehicle using paint spray particletrajectory analysis to determine a paint spray particle trajectory andimpact location according to the present invention.

[0012]FIG. 3 is a screen perspective view of a CAD model of a portion ofa vehicle.

[0013]FIG. 4 is a screen view showing cropping and sub-sampling controlsfor use with the method and system of the present invention.

[0014]FIG. 5 is a screen view showing velocity vectors along a verticalslice of a flow field over a portion of the CAD model.

[0015]FIG. 6 is a screen view showing velocity vector selection for thepresent invention.

[0016]FIG. 7 is a screen view of a dialog window for selecting paintspray gun information to be used in the present invention.

[0017]FIGS. 8A and 8B show a representative sample of particletrajectories.

[0018]FIG. 9A through 9F are perspective views of paint spray particletrajectories under varying paint spray gun operation and shaping airvelocity magnitude.

[0019]FIG. 10 is a perspective view of a system, according to thepresent invention, of analyzing paint spray particle trajectory.

DESCRIPTION OF THE PREFERRED EMBODIMENT(S)

[0020] Referring to the drawings and in particular FIG. 1, oneembodiment of a method, according to the present invention, of analyzingpaint spray particle trajectories relative to a computer aided design(CAD) model representative of a portion of a vehicle with an externalflow thereover is shown. The method is intended to be carried out on acomputer system which includes a computer having a memory, a processor,a display and user input mechanism, such as a mouse or keyboard, assubsequently described. In the present invention, the method starts inbox 10 with a CAD model of a vehicle, or a desired portion of a vehicle,which is obtained from an electronic storage device, such as a computerfile stored on a server memory, the memory of the computer, a magneticdisk storage device, or any one of numerous other electronic or magneticstorage devices. The CAD model is preferably displayed, as is known inthe art, on the display, which can be, for example, a video displayscreen.

[0021] Next, in box 12, a predetermined flow field over the CAD model,for example, representative of vehicle aerodynamics due to movementthrough the ambient is read in from an external source, for example, astored file. The external flow field may be computed by variouscommercial software programs, for example, PowerFlow™. This externalflow field is computed relative to the exterior surface of the CAD modelobtained in box 10.

[0022] Next, the method advances to block 16 where a simulated paintspray gun is placed relative to the CAD model. The paint spray gun is ofan electrostatic type having a bell cup and housing, as well as ashaping air ring (FIG. 5). The paint spray gun is preferably locatedusing an on-screen graphical user interface (GUI), in cooperation withthe user input mechanism, preferably a mouse device as is known in theart. The screen GUI and mouse device permit a user to easily anddynamically place the paint spray gun at a desired location relative tothe CAD model. It should be appreciated that more than one paint spraygun may be located relative to the CAD model and that particletrajectories emanating therefrom may be calculated and simultaneouslydisplayed, described subsequently.

[0023] The method then advances to block 18 and information is specifiedabout the particles which are simulated to be sprayed from the paintspray gun. This information may include, for example, particle size,particle velocity exiting the paint spray gun, particle density andother information describing particle characteristics. It should beappreciated that the particle information of box 18 need not be input inthe order shown in FIG. 1, but may be provided at any step of the methodprior to computation of particle trajectories in box 20. In box 20, thetrajectories are computed according to known physical principles asfurther described below, and are computed with an external velocityfield flow and electrostatic field flow.

[0024] After the particle trajectories have been computed, they aredisplayed relative to the CAD model in box 22. Various options fordisplay of the particle trajectories may be chosen, as further describedbelow, and an on-screen GUI may be used to ease user selection fromamong the display options.

[0025] Finally, in diamond 24, the user is given an option todynamically relocate the paint spray gun, preferably using the screenGUI, in order to assess the performance of a new vehicle design, or tocompare alternate vehicle designs, or to compare results from physicalaerodynamic tests and a particular vehicle design.

[0026] In the present invention, the trajectories of the paint sprayparticles of a given diameter and given initial velocity can bepredicted as in box 20 of FIG. 1 as they move through athree-dimensional (3D) flow field under the influence of aerodynamicdrag, gravity and electrostatic potential. An equation governing thetrajectory of a particle mass m and charge q, in a flow field (V_(air))and in the presence of gravity (g) and an electric field (E) is given by$\begin{matrix}{{m\frac{^{2}\overset{->}{x}}{t^{2}}} = {{q\overset{->}{E}} + {m\quad \overset{->}{g}} - {0.5\quad \rho \quad A\quad C_{d}{{\frac{\overset{->}{x}}{t} - {\overset{->}{V}}_{air}}}\left( {\frac{\overset{->}{x}}{t} - {\overset{->}{V}}_{air}} \right)}}} & (1)\end{matrix}$

[0027] where ρ is the air density, A is the cross-sectional area of aparticle which preferably is modeled as a sphere, and C_(d) is thecoefficient of drag. The details of the breakup of the paint intodroplets and surface tension effects are not included in the equation(1) as negligible, but those skilled in the art will understand thatsuch may be included if desired. If these particles are assumed to bespherical droplets with mass density ρliquid and diameter d, we canrewrite the above equation as follows: $\begin{matrix}{\frac{^{2}\overset{->}{x}}{t^{2}} = {{\frac{q}{m}\overset{->}{E}} + \overset{->}{g} - {{L\left( {\frac{\overset{->}{x}}{t} - {\overset{->}{V}}_{air}} \right)}{where}}}} & (2) \\{L = {\frac{3}{4}C_{d}{{\frac{\overset{->}{x}}{t} - {\overset{->}{V}}_{air}}}\frac{1}{\rho_{liguid}d}}} & (3)\end{matrix}$

[0028] The coefficient of drag varies depending on the relative velocityof the droplet with respect to the flow field velocity vector, V. Therelative velocity is simply the vector $\begin{matrix}{{\overset{->}{v}}_{rel} = {\frac{\overset{->}{x}}{t} - {\overset{->}{V}}_{air}}} & (4)\end{matrix}$

[0029] Accurate experimental data on the drag coefficient of spheres fora wide range of Reynolds numbers is known, and preferably a lookup tablefrom these experimental values is constructed and the method and systemof the present invention calculates the drag coefficient at eachtimestep from this table, with the Reynolds number based on the relativevelocity. Given an initial location in the flow field and a velocity ofthe paint particles, equation (2) can be solved, preferably using a 4thorder Runge-Kutta scheme, to obtain a particle trajectory. The initiallocation is specified in box 16 of FIG. 1 by locating the paint spraygun, and the initial velocity in box 18. Other trajectory computationscan be used to obtain the particle trajectories of the presentinvention.

[0030] As to the effects on paint transfer efficiency (PTE) (q/m,voltage and bell speed effects), the influence of the charge-to-massratio, q/m, on a particle trajectory can be seen in Eq. (1), where theacceleration experienced by particle is given by $\begin{matrix}{{\frac{q}{m}\overset{->}{E}} = {\frac{q}{m}{\overset{->}{\nabla}V}}} & (5)\end{matrix}$

[0031] which depends not only on the charge-to-mass ratio but also onthe gradient of the electric potential V. Subsequently, the larger theq/m ratio the larger the electrostatic force, resulting in an increasein PTE. Self-consistent fields are neglected and, therefore, theelectrostatic repulsion for larger q/m is not seen and does not modifythe PTE. A linear potential is assumed given by $\begin{matrix}{V = {{V(x)} = {V_{0}\left( \frac{x_{target} - x}{x_{target} - x_{bell}} \right)}}} & (6)\end{matrix}$

[0032] where x_(bell) is less than or equal to x, which is less than orequal to X_(target), and X_(target)−x_(bell) is the distance from thebell of the spray gun to the target (approximately 0.3 m). The potentialat the bell, therefore, is V₀ (input quantity) and decreases linearly tozero at the target. The electric potential is assumed only to vary inthe x-direction, which corresponds to the principle axis in thedirection from the bell to the target. In practice, the electricpotential is closer to exponential in nature, resulting in a larger andsmaller electric field in the near and far field regions as compared toEq. (6), respectively. The assumption of a potential field isnecessitated due to the fact that the electrostatic fields are notsolved in a self-consistent manner, i.e., solving Poisson's equationgiven a charge distribution. The initial velocity of the paint particlesis given by the rotational speed of the bell cup of the paint spray gun.FIGS. 8A and 8B show a representative sample of particle trajectories. Aparticle's tangential velocity is given by 2πNρ_(cup) wherein N is therotational speed of the bell and ρ_(cup) is the bell cup radius of thepaint spray gun. For a 30000 rpm, the particles initial velocity is onthe order of 80 m/s. For the most part, the particles leave the bell cuptangentially, as depicted in FIGS. 8A and 8B. However, due to the actualatomization, variations in the velocity are possible, resulting in aspread of velocities coming from the bell of the paint spray gun, aswell as a slight velocity component in the axial direction. Table 1contains the initial particle velocities for the range of bell speedsused, having an initial velocity of 26 m/s at 10000 rpm up to 80 m/s at30000 rpm. TABLE 4 Paint Particle Velocity Bell Speed [rpm] TangentialVelocity [m/s] 10000 26 20000 53 30000 80

[0033] As illustrated in FIGS. 9A through 9F, the sensitivity of belland shaping air speed on transfer efficiency is shown. Here, the PTE isused in a qualitative manner, i.e., any change in bell operatingconditions which increases the radius of the paint spray patterndecreases transfer efficiency with zero efficiency as having no particleimpinge the target. FIGS. 9A, 9B and 9C have bell speeds of 30000,10000, and 50000 rpm, respectively. The shaping air, charge-to-massratio, and particle diameter are 30 m/s, 5 μC/g, and 2 microns,respectively, and are held constant in FIGS. 9A though 9F. For lowspeeds, the electric force dominates the particle trajectories as shownin FIG. 9B. As the bell speed increases, the radius of trajectories,that intersect the target, increases as a result of larger initialparticle velocities. At 50000 rpm, no particles impinge upon the targetresulting in a zero transfer efficiency.

[0034]FIGS. 9D through 9F decrease the shaping air magnitude from 30 m/sto 10 m/s. These figures have been slightly rotated to view more of the3-D nature of the graphical display created by the method. Even thoughthe shaping air velocity has changed, the particle trajectories remainunchanged. The influence of the shaping air in the numerical simulationis less than that in actual experiments. Typically, 2 micron particlesimpinge the target with a small spray radius under the influence of onlythe shaping air. The numerical simulation requires an electrostaticfield in order to transfer the paint particles to the target. Thedifference lies in the numerical source region of the shaping air beingapproximately 3 mm in width as determined from the CFD. With velocitieson the order of 20 to 80 m/s, only small changes in the particletrajectories are possible over an effective collisional length of only 3to 5 mm. It should be appreciated that a more sophisticate method formodeling the shaping may be desired due to the effect of orifice flow.

[0035] Referring to FIG. 2, a method, according to the presentinvention, for enabling dynamic placement of a paint spray gun relativeto a CAD design model representative of a desired portion of a vehicleto permit visual observation of spray trajectories with respect to theCAD model with external flow thereover is shown. In box 30, a CAD modelof a vehicle is obtained as described above, which is preferablyrendered on a display screen such as that seen in FIG. 3. The CAD model(FIG. 3) may include the whole vehicle or a desired portion thereof.Next, in box 32 of FIG. 2, a flow field around the external surface ofthe CAD model is read in for the specified CAD model. The flow field ispreferably pre-computed based upon information supplied by a userregarding the particular vehicle CAD model and other external conditionsaffecting an external flow therearound. Typically, flow field dataexternal to the vehicle is computed by a CFD program, as describedabove, and such information is saved to a computer file for later usewith the method and system of the present invention.

[0036] After reading in the flow field, a rectangular box 102 may appearin the render window (FIG. 3). The box 102 shows a region in which flowfield data is available. If desired, a user can crop this box, as wellas sub-sample in it, to select only a subset of the data for the paintspray gun application, for example, by using vertical sliders 106 in acropping/sub-sampling window 108 (FIG. 4). Such allows a reduction ofthe computer memory requirements in a computer system and potentiallyenables the method and system to run faster. Additionally, atwo-dimensional slice of the external flow field can be displayed, asindicated by vectors 110 in FIG. 5, by selecting such in a velocityvector's window 112 (FIG. 6). A slice direction can be chosen to bealong any one of the coordinate axes by selecting the appropriate button(X slice, Y slice, Z slice) and the magnitude of the velocity vectorscan be controlled through a vertical slider 114 (FIG. 6).

[0037] Returning to FIG. 2, various information required for computing apaint spray trajectory is input in boxes 34 and 36. In box 34, a paintspray gun is located relative to a desired portion or target of the CADmodel. Such placement can be accomplished using a screen GUI but alsocan be placed by using dials 116, 118, 120, for the X, Y and Zcoordinates, respectively, in the main dialogue window 121 (FIG. 7). Thespray gun is displayed in the render window 122 near a target portion ofthe vehicle (FIG. 5). In box 36 of FIG. 2, various paint sprayinformation is specified. Such information is specified through the maindialogue window 121, for example, by typing in the desired dropletdiameter to box 126 and by typing the droplet mass density into box 128.In addition, the inclination angle of the paint spray gun, that is theangle of the spray measured from the horizontal, and the base angle,that is the angle of the rotation of the spray about a vertical axis,can be specified by using the sliders 130, 132, respectively, in thedialogue box 121 (FIG. 7). The trajectory of a single particle may beexamined, as can the trajectories of multiple particles in the form of aspray. The number of particles and the spray angle may be input usingbox 144 and slider 136, respectively, in the main dialogue window 121.The paint spray gun may be dynamically altered in position, slope andinclination to reflect current user selections and to provide a visualaid for assessing resulting trajectories. After the paint spray gun hasbeen positioned to a user satisfaction, trajectory calculations, withexternal flow, are performed (box 38, FIG. 2) by pressing a start button138 in the main dialogue box 121 (FIG. 7). A user may select varioustrajectories 140, 148 and 150 to be rendered. Flow steam lines which arenot affected by droplet size and which correspond to trajectories ofmassless particles, can also be rendered. These individual tracks can bedisplayed or hidden through the use of a “show/hide” button 146 in themain dialogue box 121 (FIG. 7).

[0038] Returning to FIG. 2, the diamond 44 inquires whether the paintspray gun must be modified, and if so, flow is routed to box 34 wherethe just described process of box 34 through 42 are repeated with themodified paint spray gun information. If there is not a desire to modifythe paint spray gun, then a user may request a new run in diamond 46. Ifa new run is chosen, the choice is made of picking a new vehicle indiamond 48. If a new vehicle is chosen, flow is routed to box 30 and theprocess of box 30 through 42 are repeated. However, if a new vehicle isnot chosen, the flow is routed to box 32 and the processes in boxes 34through 42 are repeated. It should be appreciated that a new vehicle orinformation re-specified if a new run is desired. It should also beunderstood that the quarter of the individual process steps of FIG. 2may be altered, and that some of the steps may be individually alteredor deleted without departing from the invention.

[0039] A representative computer system for the paint spray particletrajectory analysis method and system, according to the presentinvention, is depicted in FIG. 13. The system includes a processing unit150 connected to a user interface which may include a display terminal152, a keyboard 154, a pointing device, such as a mouse, 156, and thelike. The processing unit 150 preferably includes a central processingunit, a memory, and stored instructions, which implement a method toassist in vehicle design according to the present invention. The storedinstructions may be stored within the processing unit 150 in the memory,or in any non-volatile storage such as magnetic or optical media, EPROM,EEPROM, or the like. Alternatively, instructions may be loaded fromremoval magnetic media 160, such as a removal disk, sometimes called afloppy disk, optical media 158, or the like. In a preferred embodiment,the system includes a general purpose computer program to implement thefunctions illustrated and described with reference to FIGS. 1 through12. Of course, a system according to the present invention could also beembodied with a dedicated device, which includes various combinations ofhardware and software. The preferred embodiment may also include aprinter 162 connected to the processing unit 150, as well as a networkconnection for accessing a local server, an intranet 164, and theInternet 166.

[0040] In a preferred embodiment, the present invention includes anarithmetic logic circuit configured to retrieve information from aspecific file, display that information in a form of a vehicle design ona display screen, compute particle trajectories relative to the vehicledesign based on specific input, display the trajectories relative to thevehicle design, and allow the user to modify the specific input in orderto produce trajectories which meet the design criteria.

[0041] The present invention has been described in an illustrativemanner. It is to be understood that the terminology which has been usedis intended to be in the nature of words of description rather than oflimitation.

[0042] Many modifications and variations of the present invention arepossible in light of the above teachings. Therefore, within the scope ofthe appended claims, the present invention may be practiced other thanas specifically described.

What is claimed is:
 1. A system for designing a vehicle by enabling dynamic placement of paint spray particles into a flow domain to permit visual observation and alteration of resulting particle trajectories under a computed flow solution over a computer aided design (CAD) model representative of a desired portion of the vehicle represented on a display by a computer having memory, a processor and a user input mechanism associated therewith, said system comprising: spray gun placement code means operable with the user input mechanism to dynamically effect a desired placement of at least one paint spray gun on the display with respect to the desired portion of the CAD model; trajectory determination code means for computing at least one trajectory for a particle stream emanating from the at least one paint spray gun relative to the desired portion of the CAD model for a predetermined set of particle characteristics in a predetermined set of particle external conditions; and trajectory display code means for effecting display of the at least one trajectory with respect to the desired portion of the CAD model.
 2. A system as set forth in claim 1 wherein the spray gun placement code means includes GUI means for displaying a spray gun GUI on the display, the GUI means operative with the input mechanism for locating the desired placement of the at least one paint spray gun.
 3. A system as set forth in claim 1 wherein the predetermined set of particle characteristics includes at least one of a set of particle diameter data, particle density data, and particle initial velocity data.
 4. A system as set forth in claim 1 wherein the trajectory display code means includes code means for displaying coordinate information of the display relative to the CAD model for intersection of the at least one trajectory with the desired portion of the vehicle.
 5. A method for designing a vehicle using particle trajectory analysis with a computer aided design (CAD) model representative of the vehicle, said method comprising the steps of: preparing a CAD model of a desired portion of the vehicle; placing a paint spray gun at a desired location with respect to the desired portion of the vehicle; specifying a set of particle information describing particles to be sprayed from the paint spray gun; computing a trajectory for a particle stream emanating from the paint spray gun; displaying the trajectory relative to the desired portion of the vehicle on a display to permit visual observation thereof; and repositioning the paint spray gun if necessary to achieve a desired trajectory.
 6. A method for designing a motor vehicle by enabling dynamic placement of paint spray particles into a flow domain to permit visual observation and alteration of resulting particle trajectories with respect to a computer aided design (CAD) model representative of the vehicle, said method comprising the steps of: storing a first set of data representing a CAD model of a desired portion of the vehicle into a computer memory; displaying the first set of data on a video display screen; placing at least one paint spray gun at a desired location with respect to the desired portion of the vehicle by storing a second set of data representing the at least one paint spray gun in the computer memory; storing a third set of data in the computer memory representing particle information describing particles to be sprayed from the paint spray gun; computing a fourth set of data representing a trajectory for a particle stream emanating from the paint spray gun using the first, second and third sets of data; displaying the fourth set of data representing a trajectory relative to the first set of data representing a desired portion of the vehicle on the video display screen to permit visual observation thereof; and dynamically repositioning the paint spray gun if necessary to achieve a desired trajectory by manipulating the second set of data in the computer memory. 